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NAME: ___________________________________ ALGEBRA 293 8 – 1 Notes: Greatest Common Factor (GCF) Prime Number: A number that has exactly two factors, itself and 1. The number 1 is not prime because it only has one factor. The smallest prime number is 2. Two is also the only even prime number. Factors: Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. Product: The result of multiplying two or more factors. Example: 1 and 8 are factors of 8. 8 is the product of 1 and 8. 8 can also be factored as or as The order of the factors does not change the product. Prime factorization: When all the factors of a number are written as prime numbers. Aside from the order of the factors, there is only one way to write the prime factorization of a number. Example: Write the prime factorization of 60. 60 2 30 3 10 2 [1] 5 NAME: ___________________________________ ALGEBRA 293 8 – 1 Notes: Greatest Common Factor (GCF) Example: Write the prime factorization of 98. 98 2 49 7 7 Common factors: Factors that are shared by two or more whole numbers. Greatest Common Factor, or GCF: The greatest of these common factors Example: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 32: 1, 2, 4, 8, 16, 32 Common Factors: 1, 2, 4 Greatest Common Factor: 4 Example: Find the greatest common factor of each pair of numbers. 24 and 60 24 2 60 12 2 2 6 2 30 3 3 10 2 5 The greatest common factor is the product of the prime factors that each has in common. The greatest common factor of 24 and 60 is [2]